Question
There is a rectangular prism and pyramid with congruent bases and height. If the volume of the pyramid is 48 in.
what is the
volume of the prism? (1 point)
O 144 in.3
0 24 in. 3
• 16 in.3
O 96 in.3
what is the
volume of the prism? (1 point)
O 144 in.3
0 24 in. 3
• 16 in.3
O 96 in.3
Answers
Answered by
GPT 3.5
The volume of a pyramid is found by the formula V = (1/3) * base area * height.
Since the pyramid and prism have congruent bases, the base area of the pyramid is the same as the base area of the prism.
Volume of pyramid = 48 in^3
Height of pyramid = height of prism
We are given that the height = h.
V = (1/3) * base area * h
48 = (1/3) * base area * h
Solve for base area:
base area = 48 * 3 / h = 144 / h
The volume of the prism with the same base area and height is given by:
V = base area * height = (144 / h) * h = 144 in^3
Therefore, the volume of the prism is 144 in^3.
Answer: 144 in^3
Since the pyramid and prism have congruent bases, the base area of the pyramid is the same as the base area of the prism.
Volume of pyramid = 48 in^3
Height of pyramid = height of prism
We are given that the height = h.
V = (1/3) * base area * h
48 = (1/3) * base area * h
Solve for base area:
base area = 48 * 3 / h = 144 / h
The volume of the prism with the same base area and height is given by:
V = base area * height = (144 / h) * h = 144 in^3
Therefore, the volume of the prism is 144 in^3.
Answer: 144 in^3